幂函数阻尼系统的振动特性分析  

Analysis of vibration characteristics of power function damping system

作　　者：杨晓彤 申永军 张瑞良 YANG Xiaotong;SHEN Yongjun;ZHANG Ruiliang(School of Transportation,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;State Key Laboratory of Structural Mechanics Behavior and System Safety in Transportation Engineering,Shijiazhuang 050043,China)

机构地区：[1]石家庄铁道大学交通运输学院,石家庄050043 [2]省部共建交通工程结构力学行为与系统安全国家重点实验室,石家庄050043

出　　处：《振动与冲击》2025年第4期91-96,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(12272242);河北省省级科技计划资助(23567602H)。

摘　　要：分析了含幂函数阻尼的单自由度系统在简谐激励下的受迫振动。通过平均法与等效线性化,推导了等效线性阻尼的表达式。研究发现,非线性阻尼的减振效果与其系数和指数密切相关。进一步得到了主系统振幅和相位的定常解,通过数值仿真验证了定常解的正确性。通过等效线性阻尼的变化曲线和幅频响应曲线,分析了影响非线性阻尼减振效果的因素。研究表明,阻尼比的增加会使共振峰值左移,提高了减振性能,但需在适当范围内控制阻尼比以实现最佳减振效果。此外,阻尼比较小时阻尼指数的增加能增强阻尼作用,但过大的阻尼比会导致非线性阻尼减振效果低于线性阻尼。该研究为结构减振设计及优化提供了重要依据和理论基础。The forced vibration of a single degree⁃of⁃freedom system with power function damping under simple harmonic excitation was analyzed.The expression of equivalent linear damping was derived by averaging method and equivalent linearization.It was found that the vibration reduction effect of nonlinear damping is closely related to its coefficient and exponent.The steady⁃state solution of the amplitude and phase of the main system was further obtained,and the correctness of the steady⁃state solution was verified by numerical simulation.The factors affecting the vibration reduction effect of nonlinear damping were analyzed by the changing curve of equivalent linear damping and the amplitude⁃frequency response curve.The study shows that an increase in damping ratio will shift the resonance peak to the left and improve the vibration reduction performance,but the damping ratio needs to be controlled within an appropriate range to achieve the best vibration reduction effect.In addition,when the damping ratio is small,the increase of damping index can enhance the damping effect,but too large damping ratio will cause the vibration reduction effect of nonlinear damping to be lower than that of linear damping.This results provide an important basis and theoretical foundation for structural vibration reduction design and optimization.

关 键 词：幂函数阻尼 平均法 等效线性阻尼 振动控制 

分 类 号：O32[理学—一般力学与力学基础]